Hat Yai appeared perfectly safe to me just days ago and I am heading there now actually to spend a few beachdays in Songkhla. Expect friendly people, reasonable accommodation and a long fine sand beach plus a lot of sights around to keep You busy for at least a week. Make sure to check on Tan Kuan Hill (cablecar), the sights are fantastic from up there!
Songkhla I consider safe also for single female travelers!
In regards of beaches further south, I have been to Pattani's Panare beach area in the midst of 2008. Quite a beach with hardly any tourists but all needed amenities. Great and inexpensive food along Pattani's coast! Also worth to check out are the lengthy beaches along the gulfside shore of the peninsula stretching into Pattani Bay! Safety issues are a concern here but if you travel in a group or at least with a partner You should be able to enjoy the real South of Thailand. Be aware it is predominantly muslim area and dress not too revealing, even when sunbathing on the beaches there.
Travelers with little regard for safety and eager to maximize their beach pleasures may find "Ao Manao" Bay just south of Narathiwat town to be one of the most attractive native beaches of the kingdom. Accommodation is extremely inexpensive in Narathiwat and inhabitants here are friendly people. Food is a bit tricky unless You can resort to local chow.
To get there just take a minivan from Sungai Kolok to Narathiwat or a Songtheauw to Tak Bai, connect here with the beach side local bus to Narathiwat for a nice ride along the coast.
Me and my female partner love that area and we have spent several months there, doing a private film and documentation project.
Occasional road blocks by military or police is all You may witness about the "civil unrest" there. Check with local authorities for hints on trouble zones, these are very regional and usually disturb life only in the villages higher up in the mountains bordering Malaysia (Hala-Bala area)
Happy trails
Frank